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Rxe6 looks ok. If black plays Rxa7, white mates with Rxe8. And if he retakes with Rxe6, white mates starting with Qxa8, and if fxe6, Qxd7 finishes the win of the exchange.
Rxe6 wins easily enough.
R X e6 🙂
R x e6 🙂
1. Rxe6 fxe6
(1. .. Rxe6 2. Qxa8+ leads to back rank mate)
(1. .. Rxa7 2. Rxe8#)
2. Qxd7
Rxe6 (threat RXe8 mate)
This should win at least the bishop.
Rxe6 definitely seems to be the most promising move, and all lines I have checked from there lead to a win by white. However, black can delay the loss for quite a while, assuming the following play is reasonable:
1. Rxe6 fxe6
2. Qxd7 Rf8
3. Qxe6+ Kh8
4. Qxd5 Nc7
5. Qe5 Qxf2+
6. Kh2 Qf7
7. Rf1 Qe8
8. Rxf8+ Qxf8
9. Qxc7 Qe8
10. Ne7 h6
11. Bc6 Qf7
12. Qd8+ Kh7
13. Be4+ g6
14. Bxg6+ Qxg6
15. Nxg6 Kxg6
16. Kg3 b5
17. Qf8 Kh7
18. h4 Kg6
19. h5+ Kh7
20. Qf7+ Kh8
21. g5 hxg5
22. h6 b4
23. Qg7#
If black responds with Nc7 rather than Rf8 after Qxd7, then a shorter game results:
2. … Nc7
3. Ne7+ Kh8
4. Rd3 Qg5
5. Rf3 h5
6. Rf7 Rxe7
7. Rxe7 hxg4
8. hxg4 Qe5
9. Bf1 Qd4
10. Qxc7 Qxg4+
11. Bg2 Kh7
12. Qe5 d4
13. f3 Qg6
14. Rxe6 Qf7
15. f4 Qg6
16. Rxg6 Kxg6
17. Bd5 d3
18. Qg5+ Kh7
19. Qh5#